Home
Class 11
MATHS
Evaluate: ("lim")(xto0)(e^x-1-x)/(x^2), ...

Evaluate: `("lim")_(xto0)(e^x-1-x)/(x^2),` without using LHospitals rule and expansion f the series.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

Evaluate : lim_(xto0) (e^(x) -e^(-x))/x

Evaluate: ("lim")(xto0)(2^x-1)/((1+x)^(1/2)-1)

Evaluate : lim_(xto0) (a^(x)-b^(x))/x

Evaluate lim_(xto0) (e^(x^(2))-cosx)/(x^(2))

Evaluate: lim_(xto0)(log(e^(x)-x))/(1-cosx)

Evaluate lim_(xto0) (e^(x)+e^(-x)-2)/(x^(2))

lim_(xto0)((e^(x)-1)/x)^(1//x)

Evaluate lim_(xto0) (1-cos2x)/x^(2)

Evaluate : lim_(xto0) (1+ax)^(1//x)

Evalaute lim_(xto0) (x2^(x)-x)/(1-cosx)

CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. Evaluate: ("lim")(n→oo)x[tan^(-1)((x+1)/(x+2))-tan^(-1)(x/(x+2))]

    Text Solution

    |

  2. If ("lim")(xvecoo){(x^2+1)/(x+1)-(a x+b)}=0, then find the value of aa...

    Text Solution

    |

  3. Evaluate: ("lim")(xto0)(e^x-1-x)/(x^2), without using LHospitals rule...

    Text Solution

    |

  4. If ("lim")(x to0)(a e^x-b)/x = 2 , then find the value of a a n d bdot

    Text Solution

    |

  5. Evaluate: ("lim")(xvec1)("sin"{x})/({x}) if exists, where {x} is the f...

    Text Solution

    |

  6. Evaluate: ("lim")(xvec-2^+) (x^2-1)/(2x+4)

    Text Solution

    |

  7. Evaluate: ("lim")(nvec0)(1^(1//sin^2x)+2^(1//(sin^2x))++n^(1//sin^2x))...

    Text Solution

    |

  8. Let f(x)={cos[x],xgeq0|x|+a ,x<0 The find the value of a , so that (...

    Text Solution

    |

  9. If f(x)=|x-1|-[x], \where\ [x] is the greatest integer less then or eq...

    Text Solution

    |

  10. If y=2^(-2^((1/(1-x))) , then find lim(x->1^+)y

    Text Solution

    |

  11. Let f(x)={1+(2x)/a ,0lt=x&lt;1 and ax ,1lt=x&lt;2 If lim(x->1)f(x) e...

    Text Solution

    |

  12. Evaluate ("lim")(x->0) (sinx-2)/(cosx-1)

    Text Solution

    |

  13. (lim)(xrarr0)(sin(picos^2x)/(x^2)) is equal to (a) -pi (b) pi (c) ...

    Text Solution

    |

  14. Evaluate lim(x->0^-) (x^2-3x+2)/(x^3-2x^2)

    Text Solution

    |

  15. For x in R, lim(xrarroo)((x-3)/(x+2))^x is equal to (a) e (b) e^(-1) ...

    Text Solution

    |

  16. Evaluate lim(n-&gt;oo) [sum(r=1)^n1/2^r] , where [.] denotes the gre...

    Text Solution

    |

  17. ("lim")(xvecoo){1/(1-n^2)+2/(1-n^2)+......n/(1-n^2)}i se q u a lto 0 ...

    Text Solution

    |

  18. Evaluate ("lim")(x->(5pi)/4) [sinx+cosx], where [.] denotes the greate...

    Text Solution

    |

  19. If G(x)=-sqrt(25-x^2),t h e n lim(x->1)(G(x)-G(1))/(x-1)i s (a)1/(2...

    Text Solution

    |

  20. Evaluate the left-and right-hand limits of the function defined by f(...

    Text Solution

    |